Theorems · Theorem · probability
ProbabilityTheory.variance_add_const
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω}
[MeasureTheory.IsProbabilityMeasure μ],
MeasureTheory.AEStronglyMeasurable X μ →
∀ (c : ℝ), ProbabilityTheory.variance (fun ω => X ω + c) μ = ProbabilityTheory.variance X μ- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.univproof · cited by 3,945
- one_mulproof · cited by 2,841
- MeasureTheory.integralproof · cited by 1,779
- MeasureTheory.Integrableproof · cited by 1,367
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.Measure.realproof · cited by 530
- MeasureTheory.MemLpproof · cited by 457
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- ProbabilityTheory.variancestatement and proof · cited by 104
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_const_addproof · cited by 1
- ProbabilityTheory.variance_sub_constproof · cited by 0